Abstract
Most of the inflationary models that are in agreement with the Planck data rely on the presence of non-renormalizable operators. If the connection to low energy particle physics is made, the renormalization group (RG) introduces a sensitivity to ultraviolet (UV) physics that can be crucial in determining the inflationary predictions. We analyse this effect for the Standard Model (SM) augmented with non-minimal derivative couplings to gravity. Our set-up reduces to the SM for small values of the Higgs field, and allows for inflation in the opposite large field regime. The one-loop beta functions in the inflationary region are calculated using a covariant approach that properly accounts for the non-trivial structure of the field space manifold. We run the SM parameters from the electroweak to the inflationary scale, matching the couplings of the different effective field theories at the boundary between the two regimes, where we also include threshold corrections that parametrize effects from UV physics. We then compute the spectral index and tensor-to-scalar ratio and find that RG flow corrections can be determinant: a scenario that is ruled out at tree level can be resurrected and vice versa.
Highlights
Of the successful inflationary models, whether single or multi-field, instead rely on nonrenormalizable operators to obtain predictions in agreement with Planck
We studied the effects of the renormalization group flow on inflationary models that are embedded in low energy Standard Model theories
The inflationary predictions depend on the renormalization group equations during the inflationary stage and on a new kind of UV sensitivity [5] present in inflationary models with non-renormalizable operators
Summary
We consider the Standard Model (SM) and the Einstein-Hilbert action augmented with non-minimally derivative couplings to gravity for the Higgs, gauge and fermion fields. The summation in the gauge and fermion terms runs over the SM gauge groups and fermions respectively. For simplicity we take the non-minimal couplings for the gauge (fermion) fields universal, i.e. the same for all gauge groups (fermions), the results can be generalized. With just a constant value of the non-minimal Higgs coupling this is the original version of the new Higgs inflation proposal of ref. We parameterize the non-minimal gauge boson and fermion couplings as αi = α0iδni/2. Where we introduced the scale M2 = M mP, and with V the Standard Model Higgs potential, where we dropped the quadratic term that plays no role at large field values.
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